Enhancing community integrity of networks against multilevel targeted attacks.

The community structure and the robustness are two important properties of networks for analyzing the functionality of complex systems. The community structure is crucial to understand the potential functionality of complex systems, while the robustness is indispensable to protect the functionality of complex systems from malicious attacks. When a network suffers from an unpredictable attack, its structural integrity would be damaged. Earlier studies focused on the integrity of the node structure or the edge structure when a network suffers from a single-level malicious attack on the nodes or the edges. In this study, we model the attack on the network as a two-level targeted one. Then, we propose a community robustness index to evaluate the integrality of the community structure when the network suffers from the modeled attack. The proposed index plays an important role in analyzing the ability of the real systems to resist unpredictable failures. Finally, based on the proposed community robustness index, a greedy algorithm is devised to mitigate the network attack. Experiments on three real network systems show that with minor changes in links the community robustness of networks can be greatly improved. The results also demonstrate that the community structures in the optimized networks remain practically unchanged compared with the original ones.